模糊关系的非循环性

摘要

通过讨论模糊关系的非循环性.研究内容包括一个模糊关系及其严格部分在一个t-模T下的非循环性两部分.对模糊关系的非循环性,在T左连续下,借助α-截集和T-传递闭包,给出了T-非循环性的一些等价命题.在对模糊关系R的严格部分PR的非循环性的讨论中,主要给出了R的T-非循环性与PR的T-非循环性之间的关系以及PR的T-非循环性的一些等价命题.%In this paper,we deal with the acyclicity of fuzzy relations.The investigation is di-vided into two parts:the acyclicity of a fuzzy relation and its strict part.In the first part,several equivalent statements of T-acyclicity are given by means of α-cuts or T-transitive closure with the left continuity of T.In the second part,some properties concerning the relationships between the T-acyclicity of a fuzzy relation R and its strict part PR are investigated and equivalent statements of the T-acyclicity of PR are presented.